ACCRETION PROBLEM IN A KERR BLACK HOLE GEOMETRY VIEWED AS FLOWS IN CONVERGING–DIVERGING DUCTS

Abstract

Accretion flow on a horizon is supersonic, no matter what the flow angular momentum or the spin of the black hole is. This means that a black hole accretion can always be viewed as a flow in a flat space–time through one or more convergent–divergent ducts. In this paper, we study how the area of cross-sections must vary in order that the flow has the same properties in both systems. We show that the accretion flow experiencing a shock is equivalent to having two ducts connected back-to-back, both with a neck where the flow becomes supersonic. We study the pressure and Mach number variations for corotating, contrarotating flows and flows around a black hole with evolving spin.